But like I said: I'm not sure if the v2 API is still supported by Google, and if new keys will actually work.

Google offers these keys. On the screenshot it's visible, that the reCaptcha form is there and as I wrote also the evaluation (with and without the images) works. The mail is not sent, however. And the error is reported saying that the code should have been written. It seems to me that the Google reCaptcha is ignored here.
With the Advancedform is the case about the same. There is the built-in reCaptcha function similar to the mailform. Having both plugins installed and configured the Google reCaptcha does not show up.

CMSimple.skIt's no shame to ask for an answer if all efforts failed.
But it's awful to ask without any effort to find the answer yourself.

Thanks for the report, Ludwig! I've long given up on this plugin, though, and just archived the repo. Perhaps utaka will update his fork. Otherwise maybe someone else wants to take maintainership? In the worst case, and if really necessary, we could add it to https://github.com/cmsimple-xh.

If I remember correctly, you have to register for a specific domain to get the keys. That likely wouldn't work for localhost.

Right, that's the problem.

Actually, I have registered the cmsimple.sk and for testing used the clear172.cmsimple.sk with the same keys. On both domain and its subdomain it works. The only I can't find solution for is the styling of delivered emails. Tested with line ending *nix on/off and mail type text/html. No difference. The only place where the styling is effective is the mailfom. Not its output (sent message).

CMSimple.skIt's no shame to ask for an answer if all efforts failed.
But it's awful to ask without any effort to find the answer yourself.